Pocket Cube

Pocket Cube

The Pocket Cube is the 2x2x2 magic cube puzzle. Rubiks also sell it as the Mini Cube, and — a version with translucent cubies — the Ice Cube. Verdes sells it as the V-Cube 2. Various other brands sell it simply as a 2x2x2; for example the Eastsheen 2x2x2, Shengshou 2x2x2, LanLan 2x2x2, Ghosthand 2×2, QJ 2×2, and so on

Though one can see at a glance that it is easier than the classic 3x3x3 Rubik’s Cube, it is by no means a trivial puzzle.

With the same core symmetry as the Rubik’s Cube, but only corner pieces, it is essentially the same as the Rubik’s Cube if all you cared about was the corners. Take a Rubik’s Cube, peel off the centre stickers and the edge stickers, and you’ll have a puzzle exactly equivalent to a Pocket Cube.

According to Wikipedia (uncited), the Pocket Cube has 3674160 positions. God’s Number is 11 or 14, depending on whether you count a 180° turn as one move or two.

Variants and related puzzles

The Pocket Cube is simplest of the long series of magic cubes. From the 2×2×2 Pocket Cube, we step up to the classic 3x3x3 Rubik’s Cube, the 4x4x4 Rubik’s Revenge, the 5x5x5 Professors Cube, and so on. There are also cuboids with a non-cubic aspect; for example the 2x3x4.

Shell variants of the Pocket Cube are quite common. Because it is the simplest in the magic cube series, it is a popular choice for novelty puzzles. Hence it can be obtained in a Darth Vader shell, a Batman shell, a Homer Simpson shell, and so on.

The 2×2 Dodecahedron puzzle has a face-turning cube core, and a dodecahedron shell, yielding pyritohedral symmetry.

One particularly interesting shell variant is the 2×2 Dodecahedron, a dodecahedron puzzle that locates the turning axes of the core on six of the dodecahedron‘s edge centres. Since the core allows for 90° turns but the dodecahedron only has 180° symmetry about its edge centres, this is a jumbling puzzle. Like the Pyramorphix puzzles, it offers two puzzles in one: you can restrict yourself to 180° turns, and the puzzle will scramble without jumbling, and can be solved using only 180° turns. Or you can perform 90° turns, in which case the puzzle will jumble.

What is particularly interesting about the 2×2 Dodecahedron is the fact that only one in five edges are axes of rotation, so each pentagonal face is cut in half in only one of the five possible ways. If we think about symmetry in terms of entire pentagonal faces, every face is isometric to every other, and we have dodecahedral symmetry. But if we think about symmetry in terms of the half-pentagon stickers on each side of each faces, many symmetries disappear, and we are left with an unusual form of symmetry known as pyritohedral symmetry.